function [x, vld] = gflineq(a, b, p)vld = 0;% construct an [A, B] matrix and assign initial valueaa = [a b];x = aa(:);if ((max(x) >=p) | (min(x) < 0) | ~isempty(find(floor(x) ~= x)))    error('Element in A or B exceeded the defined field')end;[n, m] = size(aa);k = 1;i = 1;ii = [];kk = [];% forward major element selectionwhile (i <= n) & (k < m)    % make the diagonal element be one or jump one line.    while (aa(i,k) == 0) & (k < m)        ind = find(aa(i:n, k) ~= 0);        if isempty(ind)            k = k + 1;        else            indx = find(aa(i:n, k) == 1);            if isempty(indx)               ind_major = ind(1);            else               ind_major = indx(1);            end;            j = i + ind_major - 1;            tmp = aa(i, :);            aa(i,:) = aa(j, :);            aa(j, :) = tmp;        end;    end;    % clear all non-zero elements in the collumn except the major element.    if (aa(i,k) ~= 0)     % to make major element to be one.        if (aa(i,k) ~= 1)           aa(i,:) = rem(aa(i,k)^(p-2) * aa(i,:), p);        end;        ind = find(aa(:,k) ~= 0)';        ii = [ii i];        kk = [kk k];        vec = [k:m];        for j = ind            if j ~= i                % to make sure the column will be zero except the major element.                aa(j, vec) = rem(aa(j, vec) + aa(i, vec) * (p - aa(j, k)), p);            end;        end;        k = k + 1;    end;    i = i + 1;end;x = zeros(m-1, 1);% the case of no solutionif (i <= n)    % The case no solution    ind = find(aa(i:n,m) ~= 0);    if ~isempty(ind)        disp('*** Your linear equation has no solution');        return;    end;endif (rank(aa) > rank(aa(:, 1 : m-1)))    disp('*** Your linear equation has no solution');    return;end;% The solutionlen_kk = length(kk);if max(kk(1:len_kk)) > n    disp('*** Your linear equation has no solution');else    x(kk(1:len_kk)) = aa(ii(1:len_kk), m);    vld = 1;end;